Question

Prove the identify sec ×/tan × + cot ×= sin ×​

Answer 1

sec
(
x
)
tan
(
x
)
+
cot
(
x
)
=
sin
(
x
)
Start on the left side.
sec
(
x
)
tan
(
x
)
+
cot
(
x
)
Convert to sines and cosines.

Answer 2

See below

Explanation:

`\displaystyle (\sec(x))/(\tan(x)+\cot(x))\\\\=((1)/(\cos(x)))/((\sin(x))/(\cos(x))+(\cos(x))/(\sin(x)))\\\\=((1)/(\cos(x)))/((\sin^2(x)+\cos^2(x))/(\sin(x)\cos(x)))\\\\=((1)/(\cos(x)))/((1)/(\sin(x)\cos(x)))\\\\\\=(\sin(x)\cos(x))/(\cos(x))\\\\=\sin(x)`

Hence, the identity is proven